• Journal of the Korean Data and Information Science Society
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• v.14 no.2
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• pp.279-287
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• 2003

In this paper we propose a local smoothing of the Nelson type estimator for the survival function based on an approximation by the Weibull distribution function. It appears that Mean Square Error and Bias of the smoothed estimator of the Nelson type survival function estimators are significantly smaller than that of the smoothed estimator of the Kaplan-Meier survival function estimator.

• 한국데이터정보과학회:학술대회논문집
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• 2003.05a
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• pp.109-119
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• 2003

In this paper we propose a local smoothing of the Nelson type estimator for the survival function based on an approximation by the Weibull distribution function. It appears that Mean Square Error and Bias of the smoothed estimator of the Nelson type survival function estimator is significantly smaller then that of the smoothed estimator of the Kaplan-Meier survival function estimator.

• Journal of Korean Society of Water and Wastewater
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• v.34 no.4
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• pp.251-258
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• 2020

Sewer deterioration models are needed to forecast the remaining life expectancy of sewer networks by assessing their conditions. In this study, the serious defect (or condition state 3) occurrence probability, at which sewer rehabilitation program should be implemented, was evaluated using four probability distribution functions such as normal, lognormal, exponential, and Weibull distribution. A sample of 252 km of CCTV-inspected sewer pipe data in city Z was collected in the first place. Then the effective data (284 sewer sections of 8.15 km) with reliable information were extracted and classified into 3 groups considering the sub-catchment area, sewer material, and sewer pipe size. Anderson-Darling test was conducted to select the most fitted probability distribution of sewer defect occurrence as Weibull distribution. The shape parameters (β) and scale parameters (η) of Weibull distribution were estimated from the data set of 3 classified groups, including standard errors, 95% confidence intervals, and log-likelihood values. The plot of probability density function and cumulative distribution function were obtained using the estimated parameter values, which could be used to indicate the quantitative level of risk on occurrence of CS3. It was estimated that sewer data group 1, group 2, and group 3 has CS3 occurrence probability exceeding 50% at 13th-year, 11th-year, and 16th-year after the installation, respectively. For every data groups, the time exceeding the CS3 occurrence probability of 90% was also predicted to be 27th- to 30th-year after the installation.

• The Korean Journal of Applied Statistics
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• v.12 no.2
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• pp.563-572
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• 1999

수리가능한 시스템에 대한 고장시간이 여러 가지 모형에 대한 연구가 최근들어 신뢰성분야의 학자들에 의해 활발히 이루어지고 있다. 본 논문에서는 수리 가능한 시스템의 고장이 와이블과정을 따라 일어날 경우, 고장 시각 $t_n$에서의 강도함수 $\lambda$($t_n$)의 최우추정량의 분사이 형상모수인 $\beta$의 값에 따라 충분히 큰 n에 대하여 수렴 여부를 밝혔다.

• Journal of the Microelectronics and Packaging Society
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• v.18 no.1
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• pp.15-21
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• 2011

In this study, flexural strength and fracture behavior of silicon die from single crystalline silicon wafer were investigated as a function of thickness. Silicon wafers with various thickness of 300, 200, 180, 160, 150, and 100 ${\mu}m$ were prepared by mechanical grinding and polishing of as-saw wafers. Flexural strength of 40 silicon dies (size: 62.5 mm${\times}$4 mm) from each wafer was measured by four point bending test, respectively. For statistical analysis of flexural strength, shape factor(i.e., Weibull modulus) and scale factor were determined from Weibull plot. Flexural strength reflecting both statistical fracture probability and size (thickness) effect of brittle silicon die was obtained as a linear function of die thickness. Fracture appearance was discussed in relation with measured fracture strength.

• The Korean Journal of Applied Statistics
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• v.8 no.2
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• pp.133-145
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• 1995

This paper is concerned with the method of estimating lifetime distribution from field data for repairable products with multiple modes of failure, and is an extension of Bai et al.(1995). The log linear function is considered as a model for describing the relation between failure time of a product and covariates. Using the nonhomogeneous poisson process, general methods for obtaining pseudo maximum likelihood estimators(PMLEs) for the parameters are outlined and specific formulas for Weibull distribution are obtained. Effects of follow-up percentage on the PMLEs are investigated. Extension to case-cohort design is also considered.

• Proceedings of the KIEE Conference
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• 2009.07a
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• pp.2027_2028
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• 2009

본 연구에서는 한국수자원공사 고압회전기 고정자권선 절연체의 진단데이터에 대한 통계적 분석연구에 관하여 설명하고 있다. 10년 이상 수집된 진단데이터를 사용하여 와이블 함수를 이용한 누적확률을 구하였으며, 그 결과로부터 각 진단항목에 대하여 형상모수와 절연상태를 판정하는 진단기준치를 제시하였다. 그 결과로 수력발전기의 대지간 전압에 대한 부분방전량의 기준값으로 10,000pC이하를 제시하였다.

• Journal of the Korean Data and Information Science Society
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• v.23 no.6
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• pp.1195-1202
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• 2012

In this paper, we determine the expected total cost from the user's perspective for the replacement model with the extended warranty when minimal repair cost is a function of failure time. To do so, we define the extended warranty and assume the replacement model following the expiration of extended warranty from the user's perspective. Especially, we propose the criterion to buy the extended warranty and the numerical examples are presented to illustrate the purpose when the failure time of the system has a Weibull distribution.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2010.06a
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• pp.50-50
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• 2010

전력케이블의 수명예측은 전력설비의 적절한 전력설비의 신뢰성 확보에 목적이 있다. 그러나 장기간의 수명으로 설계되는 관계로 가속실험을 수행하여 중장기적인 절연성 추세를 평가하기 위해서 와이블 분포함수와 같은 통계적인 접근과 수영과 관련된 보상조건에 대한 고려가 필수적이다.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1996.04a
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• pp.719-723
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• 1996

In this research, The statistical characteristics of non-heated and nitro-carburized specimens are investigated under two stress levels (1.15 .sigma. $_{w}$ .leq. .sigma.$_{\alpha}$ .leq. 1.25 .sigma. $_{w}$). Seven specimens of each stress level are tested by rotary bending fatigue machine. The cycles about each crack length and crack propagation rate are used as statistical variagle of weibull distribution. By using concept of reliability function, reliable S-N formula of Nitro-Carburized specimen are gotten.ten.